"I feel very strongly about this," Icahn told CNBC in a Tuesday interview. "I can't promise you the stock will go up and I can't promise you they will do the buyback. But I can promise you that I'm not going away until they hear a lot more from me concerning this."

Icahn also said in the CNBC interview that his fund has built up a $2 billion investment in Apple, after originally announcing a purchase of about $1 billion of shares in August. While that represents about a half a percent of Apple's market cap, it was apparently enough to get Apple's top executives to visit his New York home for a dinner.

As is typical when Icahn tweets about a company, shares zoomed higher. Apple stock gained 2.4 percent to $487.96 Tuesday, with a noticeable spike occurring midway through the morning session, when Icahn's tweet arrived. That is less of a bump than the day Icahn announced his original investment in Apple, but the endpoint is similar: Apple shares gained 4.8 percent that day to $489.57.

Repurchasing more shares would decrease the amount of available Apple stock on the public markets, likely boosting Apple's share price in the short term, though the actual effect of increasing the buyback from $60 billion to $150 billion is not a given. Icahn termed it a "no-brainer" because of the company's strong underlying metrics and low interest rates available for Apple's to borrow money.

"They have a golden opportunity to go borrow money," Icahn told CNBC.

Analysts aren't so sure that increasing the buyback would be good for Apple's businesses: JMP Securities analyst Alex Gauna told Bloomberg News that Apple needs to focus more on revenues.

"To justify the valuation on the stock, it's got to get back to earnings growth. They have to be always innovating and putting in place the mechanisms for growth, or it doesn't matter how much cash they return to shareholders," he said.

While Apple's share price is still relatively near the same price as when Icahn, a prominent voice in the investment community since a hostile takeover of TWA in 1985, began scooping up stock, the same can't be said for the investor's other Silicon Valley gambit, Netflix. On the day that he filed notice of ownership of 5.4 million shares in Netflix, the Los Gatos video-on-demand service's stock jumped 13.9 percent to $79.24; Tuesday, Netflix shares again hit record intraday and closing prices, moving as high as $324.70 before closing with a 5 percent gain at $324.62.

"(Netflix is) not the no-brainer that it was when we first bought it," he said.

SV150 market report: Wall Street shrugs off shutdown, tech stocks lead the way

A day after declines blamed on an impending shutdown of the federal government, stocks zoomed higher on the first day of select closures due to the partisan wrangling in Washington. Technology stocks were some of main beneficiaries of Tuesday's investor largesse, with the tech-heavy Nasdaq leading Wall Street's main indexes with a 1.2 percent gain and the SV150 coming in right behind with a 1.1 percent increase.

And the widely watched Standard & Poor's 500 index: Up 46.5, or 1.23 percent, to 3,817.98

Check in weekday afternoons for the 60-Second Business Break, a summary of news from Mercury News staff writers, The Associated Press, Bloomberg News and other wire services. Contact Jeremy C. Owens at 408-920-5876; follow him at Twitter.com/jowens510.